Computer-implemented method for determining centration parameters

ABSTRACT

Centration parameters for fitting spectacle lenses to a predetermined spectacle frame and to the head of a subject are determined with a computer-implemented method. At least two calibrated images, recorded from different recording directions, of the head of the subject wearing the spectacle frame are provided, wherein geometric parameters are established by geometric position determination. The geometric parameters describe the position of the eyes and the geometry of the spectacle frame, and the centration parameters are calculated from the geometric parameters. Further, a three-dimensional model for the spectacle lenses, which are to be received in the spectacle frame, is fitted to the geometry of the geometric parameters that describe the geometry of the spectacle frame.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 16/519,562, filed Jul. 23, 2019, now U.S. patentapplication publication 2019/0346698 A1, which is a continuationapplication of international patent application PCT/EP2018/051841, filedJan. 25, 2018, which claims priority to European patent application EP17153559.4, filed on Jan. 27, 2017, all of which are hereby incorporatedby reference in their entireties.

TECHNICAL FIELD

The disclosure relates to a computer-implemented method for determiningcentration parameters, in particular for fitting spectacle lenses to agiven spectacle frame and to the head of the subject, and/or forcentring spectacle lenses, wherein at least two images of the head ofthe subject wearing a spectacle frame, which are calibrated to oneanother and recorded from different recording directions, are provided.

BACKGROUND

Centration parameters are used to correctly arrange or centre spectaclelenses in a spectacle frame, such that the spectacle lenses are arrangedat the correct position relative to the eyes of the spectacles-wearingperson. Here, these are in part anatomical parameters of the relevantperson such as the interpupillary distance, in part purelyframe-specific parameters such as the frame disk width or the frame discheight and in part combinations of anatomical and frame-specificparameters, such as the vertex distance and the fitting point height. Anoverview of conventional centration parameters is provided in DIN EN ISO13666, dated October 2013.

Uncalibrated images are recorded in known methods for determiningcentration parameters, with a measuring frame having to be fastened tothe spectacles or the spectacle frame. This is cumbersome andirritating. Further, US 2003/0123026 A1 discloses an apparatus of thetype set forth at the outset, which automatically calculates centrationparameters from images. In the known method, the spectacles are tried onvirtually. This assumes that the parameters describing the geometry ofthe spectacle frame are known in advance.

SUMMARY

It is an object of the disclosure to develop a computer-implementedmethod of the type set forth at the outset in such a way that it iseasier to carry out.

According to the disclosure, this object is achieved by acomputer-implemented method wherein a three-dimensional model for thespectacle lenses to be received in the spectacle frame is fitted to thegeometric parameters describing the geometry of the spectacle frame. Inparticular, planes or linear combinations of surfaces of n-th order arefitted to the parameters describing the geometry of the spectacle frameas an approximation for the surfaces of the spectacle lenses to bereceived in the spectacle frame and centration parameters are calculatedfrom the geometric parameters describing the position of the eyes fromthe geometric parameters describing the geometry of the spectacle frameand from the three-dimensional model.

The disclosure is based on the concept of providing a simplified modelfor the spectacle lenses to be received in the spectacle frame by virtueof parameters describing the geometry of the spectacle frame and, inparticular, parameters describing nasal and/or temporal frame edgesbeing ascertained and the model for the spectacle lenses being fitted tothese parameters. The frame edges can be approximated by straight lines.

In the process, provision is made of calibrated images. The calibrationthereof comprises the extrinsic properties of the cameras recording theimages or the camera recording the images in succession, such as therelative alignment of their optical axes and the relative alignment withrespect to one another in space, and their intrinsic properties, i.e.,the properties of the cameras themselves, which define how a point inspace, which is situated in the internal coordinate system of therespective camera, is mapped onto the coordinates of the pixels of therecorded image. A detailed description of the calibration of cameras isfound in the textbook entitled “Multiple View Geometry in ComputerVision” by Richard Hartley and Andrew Zisserman, 2nd edition, CambridgeUniversity Press 2004, and, in particular, on page 8 therein. Geometricposition determination is used to ascertain not only geometricparameters describing the position of the eyes from the images but alsogeometric parameters describing the geometry of the spectacle frame.Moreover, a three-dimensional model for the spectacle lenses to bereceived in the spectacle frame is fitted to the geometric parametersdescribing the geometry of the spectacle frame. The geometric parametersdescribing the position of the eyes, the geometric parameters describingthe geometry of the spectacle frame and the three-dimensional model areused, as alternatives to one another or in combination, for the purposesof calculating the centration parameters.

An exemplary embodiment of the method provides for planes or linearcombinations of surfaces of n-th order, in particular of at least oneplane and/or at least one paraboloid, to be fitted to the parametersdescribing the nasal and/or temporal frame edges as an approximation forthe surfaces of the spectacle lenses to be received in the spectacleframe. This represents a simplification of the model, which is easier tocalculate. Expediently, the parameters describing the nasal and temporalframe edges are ascertained by means of epipolar geometry and/or bymeans of triangulation. Here, it is typical for at least threecalibrated images of the head, which are recorded at the same time fromdifferent recording directions, to be provided, with a frontal imageimaging the head from the front and a lateral image in each case imagingthe head from the left and from the right. The recording directions ofthe lateral images each expediently include an angle of at least 60degrees, e.g., 90°±10°, with the recording direction of the frontalimage. The frontal and lateral images need not overlap in the methodaccording to the disclosure. Regions of the images possibly overlappingwith one another are expediently not used for determining the centrationparameters.

According to an exemplary embodiment, provision is made for thegeometric parameters describing the position of the eyes to include theposition of the corneal vertex in space.

According to an exemplary embodiment of the disclosure, the position ofthe corneal vertex in space, determined to a first approximation, issubjected to a correction calculation. The type of correctioncalculation then depends on the way in which the position of the cornealvertex in space is determined to the first approximation.

It is possible within the scope of a so-called pupil-based evaluationfor the position of the corneal vertex in space to be determined to afirst approximation as a point of intersection of a view ray, tangentialto the cornea, from a lateral camera recording the lateral image with aview ray, directed onto the pupil, from a frontal camera recording thefrontal image. If this is the case, the position of the corneal vertexis typically calculated according to the formula a=q+μ*v+μ*w by means ofthe correction calculation, where a denotes the position vector of thecorneal vertex in space after carrying out the correction calculation, qdenotes the position of the corneal vertex to a first approximation, μdenotes an empirical value for the distance between the pupil centre andthe corneal vertex, v denotes a unit vector in the spatial directionfrom the pupil centre to the frontal camera, and w denotes a unit vectorin the recording direction extending through the centre of a cornealsphere.

Alternatively, it is also possible to undertake a reflection-basedevaluation by virtue of a flash being produced, typically by means of anLED, when recording the images, wherein the position of the cornealvertex in space is determined to a first approximation as the positionof the reflection point of the flash on the cornea. Proceeding from thisfirst approximation, the position of the corneal vertex in thehorizontal direction proceeding from the reflection point can typicallybe calculated with the correction calculation by addingΔx=+/−r*sin(½*(arccos z/a+arctan x/(z−v))) to the x-coordinate when theflash is produced by a light source arranged centrally in front of theface of the subject, where r denotes an empirical value for the cornealradius, a denotes the distance between the optical centre of a frontalcamera recording the frontal image and the reflection point, x and zdenote the x- and z-coordinates of the reflection point in a coordinatesystem with the origin at the optical centre of the frontal camera,wherein the recording direction of the frontal camera corresponds to thez-direction and the x-direction is horizontally orthogonal to thez-direction and, when observed in the z-direction, points to the right,and v denotes the distance between the light source producing the flashand the optical centre of the frontal camera in the z-direction. Inaddition or as an alternative thereto, the position of the cornealvertex in the y-direction proceeding from the reflection point cantypically be calculated by means of the correction calculation by addingΔy=+/−r*sin ½*(arctan 1/(d−v)), where r denotes an empirical value forthe corneal radius, d denotes the distance between the optical centre ofthe frontal camera and the reflection point, v denotes the distancebetween the light source producing the flash and the optical centre ofthe frontal camera in the z-direction and l denotes the distance betweenthe light source and the optical centre of the frontal camera in they-direction, wherein the y-direction is orthogonal to the x-directionand to the z-direction and points upward in space.

Here, the plus sign in the x-direction should be applied when thecorneal vertex of the left eye from the view of the subject is detected;the minus sign should be applied to the right eye from the view of thesubject. In the y-direction, the plus sign should be applied when thelight source emitting the flash is positioned at a lower height than thefrontal camera; the minus sign should be applied when it is assembled ata greater height.

Typically, the pupil or the reflection point is detected by means offeature extraction and/or feature matching (feature comparison) and/orby means of machine learning by comparison with a multiplicity of dataknown in advance. This method step may be preceded by a face detectionand/or a detection of facial features such as the eyes as apre-processing step, in which there is a detection in respect of whichimage data belong to the face of the subject such that only these dataare included in the detection.

In order to be able to undertake the determination of the corneal vertexin space for both eyes, it is common if provision is made of at leastone calibrated third image that is recorded from a lateral position inrespect of the head at the same time as the first image and the secondimage.

Typically, the computer-implemented method according to the disclosureis carried out using an apparatus for calculating the position of thecorneal vertex as described in detail below.

The centration parameters, determined according to the disclosure, maytypically be used for centring a spectacle lens in a spectacle frameand/or for grinding a spectacle lens into a spectacle frame. Here, inone method step, the at least one spectacle lens is centred in thespectacle frame using the centration parameters determined or the atleast one spectacle lens is ground on the basis of the determinedcentration parameters for an arrangement in the spectacle frame. In thisway, it is possible to produce spectacle lenses and spectacles.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure will now be described with reference to the drawingswherein:

FIG. 1A shows an apparatus for determining centration parameters in aperspective view;

FIG. 1B shows an apparatus for determining centration parameters in aview from the front;

FIG. 2 shows an illustration of the correction calculation in the caseof a pupil-based determination of the position of the corneal vertex;

FIG. 3A shows an illustration of the correction calculation in the caseof a reflection-based determination of the position of the cornealvertex relating to a correction in the x-direction;

FIG. 3B shows an illustration of the correction calculation in the caseof a reflection-based determination of the position of the cornealvertex relating to a correction in the y-direction;

FIG. 4A shows a view from the front of a head wearing spectacles withapproximated frame edges projected thereon;

FIG. 4B shows a view from the side of a head wearing spectacles withapproximated frame edges projected thereon; and

FIG. 5 shows a schematic illustration of approximately determined lensplanes.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

The apparatus 10 illustrated in the drawing serves to determinecentration parameters for fitting spectacles. It has a column 12 which,in a height-adjustable manner, carries a camera carrier 14 which, inturn, carries a number of cameras 16 a, 16 b. In a plan view, the cameracarrier 14 is bent into an approximately circular shape and it extendsbetween two free ends 18 which are arranged at a distance from oneanother. An inner face 20 of the camera carrier 14 encloses an interior22, in which the head of a subject is situated when images are recordedby the cameras 16 a, 16 b, to the front, i.e., towards the column 12,and to the sides. In a direction extending between the free ends 18, theinner face 20 is bent in a concave manner and it has, for example, theform of a portion of a lateral face of a cylinder, wherein a cylindermay have a circular or oval base. A lifting device, not illustrated inany more detail, is arranged in the column 12 in order to be able toposition the camera carrier 14 at the correct height in relation to thehead of the subject, it being possible to move the camera carrier 14up-and-down in a motor-driven manner by way of the lifting device.

All cameras 16 a, 16 b are arranged in a camera arrangement 26 thatextends between the free ends 18. In the present exemplary embodiment,the camera arrangement 26 is embodied as a camera row 26, the cameras 16a, 16 b of which are all situated at the same height, with their opticalaxis being directed into the interior 22. In the present exemplaryembodiment, the camera row 26 comprises a frontal camera 16 a arrangedin the centre of the camera carrier 14, the optical axis of the frontalcamera being directed frontally onto the face of the subject, and eightlateral cameras 16 b that are arranged symmetrically in pairs in respectof a perpendicular plane of symmetry extending through the optical axisof the frontal camera 16 a, four of the lateral cameras being directedonto the face of the subject from the left and four being directed ontothe face of the subject from the right in each case. Moreover, thecameras 16 a, 16 b are calibrated in such a way that they are able torecord calibrated images of the subject at the same time. Thecalibration comprises the extrinsic properties, such as the relativealignment of the optical axes and the relative arrangement with respectto one another in space, and their intrinsic properties, i.e., theproperties of the cameras themselves, which define how a point in space,which is situated in the internal coordinate system of the respectivecamera, is mapped onto the coordinates of the pixels of the recordedimage.

The camera carrier 14 only encloses the interior 22 to the front,towards the column 12, and to the sides, i.e., to the left and right ofthe head of the subject. Toward the top, the bottom and toward a rearside 30, the interior is open, wherein the free ends 18 have a distancefrom one another of at least 25 cm such that the subject can comfortablyapproach from the rear side. The distance is 70 to 80 cm in the shownexemplary embodiment.

In order to illuminate the interior 22, provision is made of anillumination device having an upper light strip 32 extending above thecamera row 26 and a lower light strip 34 extending below the camera row26, the light strips having a multiplicity of LEDs as lighting means ineach case. The upper light strip 32 and the lower light strip 34 eachextend, continuously or with interruptions, over a length which is atleast as long at the length of the length of the camera row 26 asmeasured in the circumferential direction between the free ends 18. Thiscorresponds to a circumferential angle of at least 160 degrees. Near thefree ends 18, the upper light strip 32 and the lower light strip 34 areconnected to one another, in each case by a further light strip 36 thatextends in the vertical direction. Consequently, the camera row 26 isframed in the entirety thereof by at least one row of LEDs. Theapparatus 10 moreover has an open-loop or closed-loop control device,not illustrated in any more detail in the drawing, by means of which thelight intensity emitted by the LEDs can be controlled or regulateddepending on the light intensity detected by the cameras 16 a, 16 b.Here, the LEDs of the light strips 32, 34, 36 are combined into sectors,the emitted light intensities of which can be controlled or regulatedseparately from one another. Moreover, provision is made for the lightintensities emitted by the individual LEDs also to be able to becontrolled or regulated separately from one another with the open-loopor closed-loop control device.

In order to be able to correctly position the subject in the interior22, the two lateral cameras 16 b closest to the frontal camera 16 a areconfigured to measure the distance of the head of the subject from thecentre 38 of the camera carrier 14. The subject is shown whether or notthey are standing correctly by means of a display unit, which is notdisplayed in any more detail. The display unit has a plurality ofdifferently coloured light sources arranged in a row. The central lightsource lights up green when the subject stands correctly. Proceedingfrom the central light source, there is, in this sequence, a green, anorange and a red light source in each direction, the light sourcesindicating, in accordance with their colour, if the subject is slightly,clearly or much too far away from the centre 38 of the camera carrier 14or if the subject stands slightly, clearly or much too close to thecentre 38. To ensure that the recording direction of the subject isdirected to infinity when determining the centration parameters, afixation device 42 arranged at the camera carrier 14 is provided, thefixation device producing a fixation pattern in the form of a specklepattern for the subject. The fixation pattern is arranged slightlyhigher than the frontal camera 16 a so that the subject peers over thelatter. In this way, their face can be recorded to the greatest possibleextent.

The apparatus 10 is also suited, in particular, to produce an avatar ofthe head of the subject, which may be used for determining thecentration parameters. To this end, calibrated images of the head of thesubject without spectacles or spectacle frame are recorded by thecameras 16 a, 16 b. A depth profile of the head, which images the lattervery well as an approximation, is created from the images by means of asuitable process for geometric position determination, such astriangulation. The head is imaged by a multiplicity of points which canbe connected to one another with a mesh pattern or else be stored as apoint cloud. In the subsequent determination of the centrationparameters, the avatar thus ascertained may be used to determinecentration parameters which cannot be determined, or can only bedetermined approximately, on account of the geometric properties of thespectacles or the spectacle frame worn by the subject. By way ofexample, a wide frame side may cover the eye in a lateral recording tosuch an extent that the vertex distance cannot be determined or can onlybe determined very inaccurately. Moreover, tinted or strongly reflectingspectacles may not allow the eyes to be identified, or only beidentified very poorly. To counteract this, the depth profile of theavatar is projected onto the images, recorded by the cameras 16 a, 16 b,of the subject wearing the spectacles or spectacle frame and thecentration parameters, which can only be determined veryunsatisfactorily on account of the sight being restricted by thespectacles or spectacle frame, are determined by means of the image dataof the avatar. Here, for the purposes of minimizing deviations, theavatar may be fitted to the images of the subject wearing the spectaclesor spectacle frame.

The above-described apparatus 10 can be used as follows for both apupil-based detection of a corneal vertex and for a reflection-baseddetection of a corneal vertex in both eyes of the subject.

In the pupil-based method according to FIG. 2, the position of thecorneal vertex in space is initially determined to a first approximationas the point of intersection q of a first view ray 52, tangential to thecornea 50, from one of the lateral cameras 16 b recording a lateralimage of the subject with a second view ray 56, directed onto the pupil54, from a frontal camera 16 a recording a frontal image of the subject.A corrected position of the corneal vertex in space is calculated with acorrection calculation using the equation a=q+μ*v+μ*w. Here, μ is anempirical value for the distance between the pupil centre and thecorneal vertex, which typically assumes values between 2.5 mm and 4 mm.v is a unit vector in the spatial direction from the pupil centre p tothe frontal camera 16 a, the coordinates of which are specified usingthe variable c1, and it is calculated as v=(p−c1)/|p−c1|. w is a unitvector of the recording direction extending through the centre m of thecorneal sphere, the recording direction being directed onto the fixationpattern of the fixation device 42 at the spatial point t, and it iscalculated as w=(t−m)/|t−m|. All values a, q, p, c1, t, and m arethree-dimensional vectors.

Two correction calculations have to be undertaken in thereflection-based determination of the position of the corneal vertexaccording to FIGS. 3A and 3B, wherein the first correction calculation(FIG. 3A) relates to a correction in the x-direction and the secondcorrection (FIG. 3B) relates to a correction in the y-direction. Thesespatial directions are set by an internal coordinate system of thefrontal camera 16 a, which has its origin in the optical centre of thefront camera 16 a. Here, the z-direction is set by the recordingdirection of the frontal camera 16 a, the x-direction is a directionwhich extends horizontally and orthogonally with respect to thez-direction and which points to the right when observed in the directionof the latter, and the y-direction extends orthogonally to thex-direction and to the z-direction and points upward in space. In thecase of the reflection-based measurement, a flash is emitted by means ofa light source, an LED 58 in the present case, the reflection of theflash on the cornea being detected by the frontal camera 16 a and atleast one of the lateral cameras 16 b and forming the firstapproximation for the position of the corneal vertex in space. In FIGS.3A, 3B, the reflection point is denoted “approx”. In the x-direction, acorrection is undertaken by adding Δx=+/−r*sin (½*(arccos z/a+arctanx/(z−v))) to the x-coordinate of the reflection point approx, whereinthe plus sign should be used in an application to the left eye and theminus sign should be used in an application to the right eye (cf. FIG.3a ). Here, r is an empirical value for the corneal radius, which istypically approximately 8 mm. a is the distance of the optical centre ofthe frontal camera 16 a from the reflection point approx and v is thedistance of the LED 58 from the optical centre of the frontal camera 16a in the z-direction. Once again, x and z are the coordinates in the x-and z-directions.

In the y-direction, a correction is undertaken by adding Δy=+/−r*sin½*(arctan 1/(d−v)), proceeding from the reflection point approx. Onceagain, r is the empirical value for the corneal radius, d is thedistance of the optical centre of the frontal camera 16 a from thereflection point approx in the z-direction, v is the distance of the LED58 from the optical centre of the frontal camera 16 a in the z-directionand l is the distance of the LED 58 from the optical centre of thefrontal camera 16 a in the y-direction. The plus sign is used when theLED 58 is arranged below the frontal camera 16 a, i.e., if they-coordinate of the LED 58 is smaller than the y-coordinate of thefrontal camera 16 a or of the optical centre of the latter. The minussign is used if the LED is arranged above the frontal camera 16 a.

In the above-described method, the pupil or the reflection point approxcan be detected, for example, by means of feature extraction and/orfeature matching and/or by means of machine learning by comparison witha multiplicity of data known in advance. This detection step can bepreceded by a step in which a face detector identifies which pixelsbelong to the face of the subject or to their eye area such that therecan already be a restricted search for the pupil or the reflection pointapprox.

The position of the corneal vertex in space is used for determining thecentration parameters when fitting the spectacles. By means of thecalibrated images recorded by the cameras 16 a, 16 b, geometricparameters describing the geometry of the spectacle frame areascertained by geometric position determination, in particular bytriangulation or epipolar geometry. The parameters comprise the nasaland temporal frame edges 60, 62, as indicated in FIGS. 4A and 4B inexemplary fashion. Planes 64 are fitted to the parameters describing thenasal and temporal frame edges 60, 62, as an approximation for thesurfaces of the spectacle lenses to be received in the spectacle frame.FIG. 5 schematically shows the planes 64 in front of the respective,approximately represented cornea 66 with schematically illustratedvisual beams 68 of the cameras 16 a, 16 b. Finally, the centrationparameters are calculated from the data obtained.

The foregoing description of the exemplary embodiments of the disclosureillustrates and describes the present invention. Additionally, thedisclosure shows and describes only the exemplary embodiments but, asmentioned above, it is to be understood that the disclosure is capableof use in various other combinations, modifications, and environmentsand is capable of changes or modifications within the scope of theconcept as expressed herein, commensurate with the above teachingsand/or the skill or knowledge of the relevant art.

The term “comprising” (and its grammatical variations) as used herein isused in the inclusive sense of “having” or “including” and not in theexclusive sense of “consisting only of.” The terms “a” and “the” as usedherein are understood to encompass the plural as well as the singular.

All publications, patents and patent applications cited in thisspecification are herein incorporated by reference, and for any and allpurposes, as if each individual publication, patent or patentapplication were specifically and individually indicated to beincorporated by reference. In the case of inconsistencies, the presentdisclosure will prevail.

The invention claimed is:
 1. A computer-implemented method fordetermining centration parameters, the method comprising: providing atleast two images of a head of a subject wearing a spectacle frame, theat least two images being calibrated to one another and recorded fromdifferent recording directions; ascertaining geometric parametersdescribing a position of eyes of the subject from the at least twoimages by geometric position determination; fitting a three-dimensionalmodel for spectacle lenses to be received in a spectacle frame togeometric parameters describing a geometry of the spectacle frame,wherein at least one of planes or linear combinations of surfaces ofn-th order are fitted to the geometric parameters) describing thegeometry of the spectacle frame as an approximation for the surfaces ofthe spectacle lenses to be received in the spectacle frame; calculatingcentration parameters from the geometric parameters describing theposition of the eyes, the geometric parameters describing the geometryof the spectacle frame, and the three-dimensional model, wherein thegeometric parameters describing the position of the eyes include aposition of a corneal vertex in space; and determining the position ofthe corneal vertex in space to a first approximation as a point ofintersection q of a first view ray, tangential to the cornea, from alateral camera recording the lateral image with a second view ray,directed onto the pupil, from a frontal camera recording the frontalimage.
 2. The computer-implemented method according to claim 1, whereinthe surfaces of n-th order comprise a plane, a paraboloid, or the planeand the paraboloid.
 3. The computer-implemented method according toclaim 1, wherein a plane is respectively fitted to the parametersdescribing the geometry of the spectacle frame as an approximation forthe surface of each of the spectacle lenses to be received in thespectacle frame or each spectacle frame edge receiving the spectaclelenses.
 4. The computer-implemented method according to claim 1, whereinthe at least two images are recorded at a same time.
 5. Thecomputer-implemented method according to claim 1, wherein the geometricparameters describing the geometry of the spectacle frame includeparameters describing nasal and/or temporal frame edges approximated bystraight lines, and wherein the three-dimensional model is fitted to theparameters describing the nasal and/or temporal frame edges.
 6. Thecomputer-implemented method according to claim 1, further comprising:providing at least three images of the head of the subject wearing thespectacle frame, the at least three images being calibrated to oneanother and recorded at a same time from different recording directions,wherein a frontal image images the head from a front side, a leftlateral image images the head from a left side, and a right lateralimage images the head from a right side.
 7. The computer-implementedmethod according to claim 6, wherein the recording directions of theleft and right lateral images each include an angle of more than 60degrees and no more than 120 degrees with the recording direction of thefrontal image.
 8. The computer-implemented method according to claim 1,wherein the at least two images do not overlap or wherein the centrationparameters are determined only from non-overlapping regions of the atleast two images.
 9. The computer-implemented method according to claim1, further comprising: performing a correction calculation of theposition of the corneal vertex.
 10. A computer-implemented method fordetermining centration parameters, the method comprising: providing atleast two images of a head of a subject wearing a spectacle frame, theat least two images being calibrated to one another and recorded fromdifferent recording directions; ascertaining geometric parametersdescribing a position of eyes of the subject from the at least twoimages by geometric position determination; fitting a three-dimensionalmodel for spectacle lenses to be received in a spectacle frame togeometric parameters describing a geometry of the spectacle frame,wherein at least one of planes or linear combinations of surfaces ofn-th order are fitted to the geometric parameters) describing thegeometry of the spectacle frame as an approximation for the surfaces ofthe spectacle lenses to be received in the spectacle frame; calculatingcentration parameters from the geometric parameters describing theposition of the eyes, the geometric parameters describing the geometryof the spectacle frame, and the three-dimensional model, wherein thegeometric parameters describing the position of the eyes include aposition of a corneal vertex in space, and wherein the correctioncalculation comprises calculating the corneal vertex according toa=q+μ*v+μ*w, where a denotes the position vector of the corneal vertexin space after carrying out the correction calculation, q denotes theposition of the corneal vertex to a first approximation, μ denotes anempirical value or an actual value for the distance between the pupilcentre and the corneal vertex, v denotes a unit vector in the spatialdirection from the pupil centre to the frontal camera, and w denotes aunit vector in the recording direction extending through the centre of acorneal sphere.
 11. A computer-implemented method for determiningcentration parameters, the method comprising: providing at least twoimages of a head of a subject wearing a spectacle frame, the at leasttwo images being calibrated to one another and recorded from differentrecording directions; ascertaining geometric parameters describing aposition of eyes of the subject from the at least two images bygeometric position determination; fitting a three-dimensional model forspectacle lenses to be received in a spectacle frame to geometricparameters describing a geometry of the spectacle frame, wherein atleast one of planes or linear combinations of surfaces of n-th order arefitted to the geometric parameters describing the geometry of thespectacle frame as an approximation for the surfaces of the spectaclelenses to be received in the spectacle frame; calculating centrationparameters from the geometric parameters describing the position of theeyes, the geometric parameters describing the geometry of the spectacleframe, and the three-dimensional model; producing a flash when recordingthe images; and determining the position of the corneal vertex in spaceto a first approximation as the position of the reflection point of theflash on the cornea.
 12. A computer-implemented method for determiningcentration parameters, the method comprising: providing at least twoimages of a head of a subject wearing a spectacle frame, the at leasttwo images being calibrated to one another and recorded from differentrecording directions; ascertaining geometric parameters describing aposition of eyes of the subject from the at least two images bygeometric position determination; fitting a three-dimensional model forspectacle lenses to be received in a spectacle frame to geometricparameters describing a geometry of the spectacle frame, wherein atleast one of planes or linear combinations of surfaces of n-th order arefitted to the geometric parameters describing the geometry of thespectacle frame as an approximation for the surfaces of the spectaclelenses to be received in the spectacle frame; and calculating centrationparameters from the geometric parameters describing the position of theeyes, the geometric parameters describing the geometry of the spectacleframe, and the three-dimensional model, wherein the geometric parametersdescribing the position of the eyes include a position of a cornealvertex in space, wherein the position of the corneal vertex in ahorizontal direction proceeding from the reflection point is calculatedwith the correction calculation by adding Δx=+/−r*sin (½*(arccosz/a+arctan x/(z−v))) to the x-coordinate, where r denotes an empiricalvalue or an actual value for the corneal radius, a denotes the distancebetween the optical centre of a frontal camera recording the frontalimage and the reflection point, x and z denote the x- and z-coordinatesof the reflection point in a coordinate system with the origin at theoptical centre of the frontal camera, and wherein the recordingdirection of the frontal camera corresponds to the z-direction and thex-direction is horizontally orthogonal to the z-direction and, whenobserved in the z-direction, points to the right, and v denotes thedistance between the light source producing the flash and the opticalcentre of the frontal camera in the z-direction.
 13. Acomputer-implemented method for determining centration parameters, themethod comprising: providing at least two images of a head of a subjectwearing a spectacle frame, the at least two images being calibrated toone another and recorded from different recording directions;ascertaining geometric parameters describing a position of eyes of thesubject from the at least two images by geometric positiondetermination; fitting a three-dimensional model for spectacle lenses tobe received in a spectacle frame to geometric parameters describing ageometry of the spectacle frame, wherein at least one of planes orlinear combinations of surfaces of n-th order are fitted to thegeometric parameters) describing the geometry of the spectacle frame asan approximation for the surfaces of the spectacle lenses to be receivedin the spectacle frame; and calculating centration parameters from thegeometric parameters describing the position of the eyes, the geometricparameters describing the geometry of the spectacle frame, and thethree-dimensional model, wherein the geometric parameters describing theposition of the eyes include a position of a corneal vertex in space,wherein the position of the corneal vertex in the y-direction proceedingfrom the reflection point is calculated with the correction calculationby adding Δy=+/−r*sin ½*(arctan 1/(d−v)), where r denotes an empiricalvalue or an actual value for the corneal radius, d denotes the distancebetween the optical centre of the frontal camera and the reflectionpoint in the z-direction, v denotes the distance between the lightsource producing the flash and the optical centre of the frontal camerain the z-direction and l denotes the distance between the light sourceand the optical centre of the frontal camera in the y-direction, andwherein the y-direction is orthogonal to the x-direction and to thez-direction and points upward in space.
 14. A computer program stored ona non-transitory storage medium with program code for carrying out themethod according to claim 1 when the computer program is loaded onto acomputer and/or executed on the computer.
 15. A method of operating anapparatus for carrying out the computer-implemented method according toclaim 1, wherein the apparatus has a camera carrier configured to partlyenclose an interior that is open to the top, to the bottom, and to arear side, wherein the camera carrier carries at least three camerasthat are arranged between two free ends of the camera carrier anddirected toward the interior, and wherein the camera carrier has anillumination device configured to illuminate the interior.
 16. A methodfor centring at least one spectacle lens in a spectacle frame, themethod comprising: determining centration parameters of the at least onespectacle lens with the method according to claim 1; and centring the atleast one spectacle lens in the spectacle frame with the determinedcentration parameters.
 17. A method for grinding at least one spectaclelens into a spectacle frame, wherein centration parameters aredetermined with the method according to claim 1, and wherein the atleast one spectacle lens is ground on the basis of the determinedcentration parameters for an arrangement in the spectacle frame.
 18. Amethod for producing a spectacle lens comprising: grinding the spectaclelens into a spectacle frame according to the method of claim
 17. 19. Amethod for producing spectacles, the method comprising: centring atleast one spectacle lens in a spectacle frame according to the method ofclaim
 16. 20. An apparatus for determining centration parameters forfitting spectacle lenses to a given spectacle frame and to a head of asubject, the apparatus comprising: a first camera configured to record afirst image from a first viewing direction; at least one second camera,calibrated to the first camera, configured to record a second image froma second viewing direction that differs from the first viewingdirection; and a computer having a processor configured to execute acomputer program and a non-transitory memory in which the computerprogram is stored, the computer program having program code that, whenexecuted by the processor, causes the apparatus to: provide at least twoimages of the head of a subject wearing a spectacle frame, which arecalibrated to one another and recorded from different viewingdirections, ascertain geometric parameters describing the position ofthe eyes and geometric parameters describing the geometry of thespectacle frame, from the images by geometric position determination,fit a three-dimensional model for spectacle lenses to be received in aspectacle frame to geometric parameters describing a geometry of thespectacle frame, wherein at least one of planes or linear combinationsof surfaces of n-th order are fitted to the geometric parametersdescribing the geometry of the spectacle frame as an approximation forthe surfaces of the spectacle lenses to be received in the spectacleframe; calculate centration parameters from the geometric parametersdescribing the position of the eyes, the geometric parameters describingthe geometry of the spectacle frame, and the three-dimensional model,wherein the geometric parameters describing the position of the eyesinclude a position of a corneal vertex in space; and determine theposition of the corneal vertex in space to a first approximation as apoint of intersection q of a first view ray, tangential to the cornea,from a lateral camera recording the lateral image with a second viewray, directed onto the pupil, from a frontal camera recording thefrontal image.
 21. A computer program stored on a non-transitory storagemedium with program code for carrying out the method according to claim10 when the computer program is loaded onto a computer and/or executedon the computer.
 22. A computer program stored on a non-transitorystorage medium with program code for carrying out the method accordingto claim 11 when the computer program is loaded onto a computer and/orexecuted on the computer.
 23. A computer program stored on anon-transitory storage medium with program code for carrying out themethod according to claim 12 when the computer program is loaded onto acomputer and/or executed on the computer.
 24. A computer program storedon a non-transitory storage medium with program code for carrying outthe method according to claim 13 when the computer program is loadedonto a computer and/or executed on the computer.
 25. An apparatus fordetermining centration parameters for fitting spectacle lenses to agiven spectacle frame and to a head of a subject, the apparatuscomprising: a first camera configured to record a first image from afirst viewing direction; at least one second camera, calibrated to thefirst camera, configured to record a second image from a second viewingdirection that differs from the first viewing direction; and a computerhaving a processor configured to execute a computer program and anon-transitory memory in which the computer program is stored, thecomputer program having program code that, when executed by theprocessor, causes the apparatus to perform the method according to claim10.
 26. An apparatus for determining centration parameters for fittingspectacle lenses to a given spectacle frame and to a head of a subject,the apparatus comprising: a first camera configured to record a firstimage from a first viewing direction; at least one second camera,calibrated to the first camera, configured to record a second image froma second viewing direction that differs from the first viewingdirection; and a computer having a processor configured to execute acomputer program and a non-transitory memory in which the computerprogram is stored, the computer program having program code that, whenexecuted by the processor, causes the apparatus to perform the methodaccording to claim
 11. 27. An apparatus for determining centrationparameters for fitting spectacle lenses to a given spectacle frame andto a head of a subject, the apparatus comprising: a first cameraconfigured to record a first image from a first viewing direction; atleast one second camera, calibrated to the first camera, configured torecord a second image from a second viewing direction that differs fromthe first viewing direction; and a computer having a processorconfigured to execute a computer program and a non-transitory memory inwhich the computer program is stored, the computer program havingprogram code that, when executed by the processor, causes the apparatusto perform the method according to claim
 12. 28. An apparatus fordetermining centration parameters for fitting spectacle lenses to agiven spectacle frame and to a head of a subject, the apparatuscomprising: a first camera configured to record a first image from afirst viewing direction; at least one second camera, calibrated to thefirst camera, configured to record a second image from a second viewingdirection that differs from the first viewing direction; and a computerhaving a processor configured to execute a computer program and anon-transitory memory in which the computer program is stored, thecomputer program having program code that, when executed by theprocessor, causes the apparatus to perform the method according to claim13.